YES

(VAR x0 x1 x2)
(RULES
  multiply(multiply(x0,x1),x2) -> multiply(x0,multiply(x1,x2))
  inverse(multiply(x0,x1)) -> multiply(inverse(x1),inverse(x0))
  multiply(inverse(x0),multiply(x0,x1)) -> x1
  multiply(x0,multiply(inverse(x0),x1)) -> x1
  double_divide(x1,x0) -> multiply(inverse(x1),inverse(x0))
  multiply(x0,identity()) -> x0
  multiply(x1,inverse(x1)) -> identity()
  inverse(inverse(x0)) -> x0
  inverse(identity()) -> identity()
  multiply(identity(),x0) -> x0
  multiply(inverse(x0),x0) -> identity()
)

(COMMENT
Termination is shown by KBO with weight

  w0 = 1
  w(double_divide) = 1
  w(identity) = 1
  w(multiply) = 0
  w(inverse) = 0

and precedence:

  inverse > multiply > double_divide > identity
)